Question: "Consider each distribution. Determine if it is a..."

europaparksn

Answered question

2021-12-04

Consider each distribution. Determine if it is a valid probability distribution or not, and explain your answer.

\begin{array}{cc} x & 0 & 1 & 2 \\ P (x) & 0.25 & 0.60 & 0.15 \end{array}

Answer & Explanation

Clara Clark

Beginner2021-12-05Added 17 answers

Step 1
The provided distribution is:

\begin{array}{cc} x & 0 & 1 & 2 \\ P (x) & 0.25 & 0.60 & 0.15 \end{array}

Step 2
The expected value can be calculated as:

E (X) = \sum_{x} x p (x)

= 0 \times 0.25 + 1 \times 0.60 + 2 \times 0.15

= 0.9

Step 3
The standard deviation (S.D) can be calculated as:

V (X) = \sum (x - E (x)))^{2} p (x)

= {(0 - 0.90)}^{2} 0.25 + {(1 - 0.90)}^{2} 0.60 + {(2 - 0.90)}^{2} 0.15

= 0.39

S . D = \sqrt{0.39}

= 0.6245

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